String Shifting

AtCoder

IDabc223_b

Time2000ms

Memory256MB

Difficulty—

On a non-empty string, a **left shift** moves the first character to the end of the string, and a **right shift** moves the last character to the beginning of the string. For example, a left shift on `abcde` results in `bcdea`, and two right shifts on `abcde` result in `deabc`. You are given a non-empty $S$ consisting of lowercase English letters. Among the strings that can be obtained by performing zero or more left shifts and zero or more right shifts on $S$, find the lexicographically smallest string and the lexicographically largest string. What is the lexicographical order?Simply speaking, the lexicographical order is the order in which words are listed in a dictionary. As a more formal definition, here is the algorithm to determine the lexicographical order between different strings $S$ and $T$. Below, let $S_i$ denote the $i$\-th character of $S$. Also, if $S$ is lexicographically smaller than $T$, we will denote that fact as $S \lt T$; if $S$ is lexicographically larger than $T$, we will denote that fact as $S \gt T$. 1. Let $L$ be the smaller of the lengths of $S$ and $T$. For each $i=1,2,\dots,L$, we check whether $S_i$ and $T_i$ are the same. 2. If there is an $i$ such that $S_i \neq T_i$, let $j$ be the smallest such $i$. Then, we compare $S_j$ and $T_j$. If $S_j$ comes earlier than $T_j$ in alphabetical order, we determine that $S \lt T$ and quit; if $S_j$ comes later than $T_j$, we determine that $S \gt T$ and quit. 3. If there is no $i$ such that $S_i \neq T_i$, we compare the lengths of $S$ and $T$. If $S$ is shorter than $T$, we determine that $S \lt T$ and quit; if $S$ is longer than $T$, we determine that $S \gt T$ and quit. ## Constraints * $S$ consists of lowercase English letters. * The length of $S$ is between $1$ and $1000$ (inclusive). ## Input Input is given from Standard Input in the following format: $S$ [samples]

Samples

Input #1

aaba

Output #1

aaab
baaa

By performing shifts, we can obtain four strings: `aaab`, `aaba`, `abaa`, `baaa`. The lexicographically smallest and largest among them are `aaab` and `baaa`, respectively.

Input #2

Output #2

z
z

Any sequence of operations results in `z`.

Input #3

abracadabra

Output #3

aabracadabr
racadabraab

API Response (JSON)

{
  "problem": {
    "name": "String Shifting",
    "description": {
      "content": "On a non-empty string, a **left shift** moves the first character to the end of the string, and a **right shift** moves the last character to the beginning of the string. For example, a left shift on ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc223_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "On a non-empty string, a **left shift** moves the first character to the end of the string, and a **right shift** moves the last character to the beginning of the string.\nFor example, a left shift on ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments